Problem: $78$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $12$ less than $2$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 78}$ ${x = 2y-12}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${2y-12}$ for $x$ in the first equation. ${(2y-12)}{+ y = 78}$ Simplify and solve for $y$ $ 2y-12 + y = 78 $ $ 3y-12 = 78 $ $ 3y = 90 $ $ y = \dfrac{90}{3} $ ${y = 30}$ Now that you know ${y = 30}$ , plug it back into ${x = 2y-12}$ to find $x$ ${x = 2}{(30)}{ - 12}$ $x = 60 - 12$ ${x = 48}$ You can also plug ${y = 30}$ into ${x+y = 78}$ and get the same answer for $x$ ${x + }{(30)}{= 78}$ ${x = 48}$ There were $48$ home team fans and $30$ away team fans.